Question

Find the coordinates of the third vertex of the triangle ABC, if A(-5, -7) , B(4, -3) and the coordinate of the centroid lies at (-1, 2).

Answer 1

Answer:

(-2, 16)

Step-by-step explanation:

Hi,

If the given vertices of triangle are A(x₁, y₁), B(x₂, y₂) and C(x₃, y₃), then the

centroid of the triangle is given by G(x₁ + x₂ + x₃/3,  y₁ + y₂ + y₃/3).

Given vertices of triangle are A(-5, -7) and B(4, -3).

Hence, centroid of the triangle will be ( -5 +4 + x₃/3, -7 -3 + y₃/3)

But given centroid as (-1, 2)

=> ( -5 +4 + x₃/3, -7 -3 + y₃/3) = (-1, 2).

By equating each component we get,

-5 +4 + x₃/3 = -1 and -7 -3 + y₃/3 = 2

=> x₃ = -2 and y₃ = 16

Thus, the coordinates of the vertex C are (-2, 16).

Hope, it helped !

Answer 2

Answer:

The coordinates of centroid (x,y) of a triangle are

x=

3

x

1

+x

2

+x

3

y=

3

y

1

+y

2

+y

3

In the given problem,

(x

1

,y

1

)=(3,−5)

(x

2

,y

2

)=(−7,4)

(x

3

,y

3

)=?

(x,y)=(2,−1)

So,

2=

3

3−7+x

3

6=−4+x

3

x

3

=6+4=10

And

−1=

3

−5+4+y

3

−3=−1+y

3

y

3

=−3+1=−2